Answer
$5x^2\sqrt{2}$
Work Step by Step
RECALL:
(1) The quotient rule:
$\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$
where
$\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$
(2) $\dfrac{a^m}{a^n} = a^{m-n}, a \ne =0$
Use the quotient rule above to obtain:
$\require{cancel}=\sqrt{\dfrac{500x^3}{10x^{-1}}}
\\=\sqrt{\dfrac{50\cancel{500}x^3}{\cancel{10}x^{-1}}}
\\=\sqrt{\dfrac{50x^3}{x^{-1}}}$
Use rule (2) above to obtain:
$=\sqrt{50x^{3-(-1)}}
\\=\sqrt{50x^{3+1}}
\\=\sqrt{50x^4}$
Factor the radicand so that at least one factor is a perfect square to obtain:
$=\sqrt{25x^4(2)}
\\=\sqrt{(5x^2)^2(2)}$
Simplify to obtain:
$=5x^2\sqrt{2}$
